Yes you can!
You can use Yousician on mobile devices (iOS, Android) and computers (Mac, PC, Linux). Simply make sure to log in with the same account credentials - username (case sensitive) or email and your password. Please do not forget to log out on the previous device to make sure your progress is transferred.
When installing desktop version, if you already have an account click "download installer" below the big "create account" button, please do not create a new account again (unless you would like to have another one).